Profit, revenue and cost are related, and can be calculated from one another.
- The profit function is
- The domain of the profit function is x > 0
- The profit when producing 60 items is 1650
- The profit when producing 70 items is 1600
The cost function is given as:
The revenue function is given as:
<u>(a) Calculate the profit function</u>
This is calculated using:
So, we have:
Evaluate like terms
<u>(b) The domain of the profit function</u>
When profit is 0 or less, then it becomes no profit.
Hence, the domain of the profit function is x > 0
<u>(c) The profit for 60 and 70 items</u>
Substitute 60 and 70 for x in P(x)
The profit when producing 60 items is 1650
The profit when producing 70 items is 1600
<u>(d) Why producing 10 more units less profit</u>
When a function reaches the optimal value, the value of the function begins to reduce.
This means that, producing 10 more units takes the profit function beyond its maximum point.
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